Periodic and Sturmian languages
نویسندگان
چکیده
Counting the number of distinct factors in the words of a language gives a measure of complexity for that language similar to the factor-complexity of infinite words. Similarly as for infinite words, we prove that this complexity functions f(n) is either bounded or f(n) ≥ n+1. We call languages with bounded complexity periodic and languages with complexity f(n) = n + 1 Sturmian. We describe the structure of periodic languages and we characterize the Sturmian languages as the sets of factors of (oneor two-way) infinite Sturmian words.
منابع مشابه
More on the dynamics of the symbolic square root map
In our earlier paper [A square root map on Sturmian words, Electron. J. Combin. 24.1 (2017)], we introduced a symbolic square root map. Every optimal squareful infinite word s contains exactly six minimal squares and can be written as a product of these squares: s = X2 1X 2 2 · · · . The square root √ s of s is the infinite word X1X2 · · · obtained by deleting half of each square. We proved tha...
متن کاملThe sequence of open and closed prefixes of a Sturmian word
A finite word is closed if it contains a factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We are interested in the ocsequence of a word, which is the binary sequence whose n-th element is 0 if the prefix of length n of the word is open, or 1 if it is closed. We exhibit results showing that this sequence is deeply related to the co...
متن کاملSturmian Canons
Sturmian words are balanced, almost periodic, self-similar and hierarchical infinite sequences that have been studied in music theory in connection with diatonic scale theory and related subjects.[3][5] Carey and Camplitt 1996 give a brief but suggestive rhythmic example in which these properties are made manifest in a particularly visceral manner. The present paper expands upon this example, c...
متن کاملA Square Root Map on Sturmian Words
We introduce a square root map on Sturmian words and study its properties. Given a Sturmian word of slope α, there exists exactly six minimal squares in its language (a minimal square does not have a square as a proper prefix). A Sturmian word s of slope α can be written as a product of these six minimal squares: s = X2 1X 2 2X 2 3 · · · . The square root of s is defined to be the word √ s = X1...
متن کاملSturmian numeration systems and decompositions to palindromes
We extend the classical Ostrowski numeration systems, closely related to Sturmian words, by allowing a wider range of coefficients, so that possible representations of a number n better reflect the structure of the associated Sturmian word. In particular, this extended numeration system helps to catch occurrences of palindromes in a characteristic Sturmian words and thus to prove for Sturmian w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Inf. Process. Lett.
دوره 98 شماره
صفحات -
تاریخ انتشار 2006